Simple machines: pulleys

By Smacaroni, Posted May 26, 2011

Not bike related, but I figure this is probably the best place to ask without having to register somewhere else. I'm willing to bet a middle school student could answer this, but that's been a few years for me. I seem to remember, a single pulley only changes direction, no mechanical advantage.

Let's say you have a single pulley system:

_B_

@

/ \

C A

Where B is the fixed pulley support, C is the load and A is point where force is applied to the cable.

Assuming no friction, is the force applied at point B the same as it is at A? (I remember something about 180 degrees is a ~.33 mew?)

So there would be no difference if the point at B were a mounting point and A were a force equal to the force at A in the above example, assuming there were a cable connecting A and B?

By RiverReaper, Posted May 26, 2011

By Smacaroni, Posted May 26, 2011

By grayracer513, Posted May 26, 2011

By Smacaroni, Posted May 26, 2011

Darn, thanks, now I'm confused again.

So this means point B in my above example is under double the force of A when it's a pulley and equal stress when it's just a cable?

Ok, this is what I want to do.

The "normal" set up for a seat belt is the belt is tied to the frame at four points. In the driver's side, you have a point on the outside at the floor, a point inside at the floor, a point above the shoulder on the outside and again at the floor.

If this changes so there's only three points of contact, one above the shoulder, one at the outside floor and on on the inside floor, is the stress on the shoulder point any different than before in the event of an accident? The contact area over the body would be the same.

My thinking is that point above the shoulder is under the same stresses regardless of if the belt runs back down to the floor again or not.

Converting a two-point harness into a three point harness. There's already a factory mounting point above the shoulder, it just wasn't used standard and most people didn't pay for the option.

By msiddalingaiah, Posted May 26, 2011

Here's a simple way to think about it: energy is always conserved, always.

energy = force x distance

If one end of a rope or pulley moves twice as far, it must have half the force.

By grayracer513, Posted May 26, 2011

So this means point B in my above example is under double the force of A when it's a pulley and equal stress when it's just a cable?

The picture you pasted in the quoted post shows the pulley as F and each lead as 1/2 F (F/2). This is true when either lead is anchored and force applied to the other. However, both leads share the totality of the load (W in the drawings) whether anything moves or not:

But the load bearing pulley there is moveable. The specific example you give of the shoulder belt in a typical OEM 3 point car harness is a fixed pulley system:

If the pulley is the third anchor point above the shoulder, the red arrow is the retractor, and the weight is the load placed on the end of the belt at the buckle by the wearer. So yes, whatever load is borne by the lead running from the buckle to the point above the shoulder is also carried by the "pulley" and the retractor, and the lead between.

By Smacaroni, Posted May 26, 2011

so by eliminating the second floor connection, is the force applied to the shoulder harness point different in a collision? I'm pretty sure it's no, but I'd like confirmation.

By grayracer513, Posted May 26, 2011

so by eliminating the second floor connection, is the force applied to the shoulder harness point different in a collision? I'm pretty sure it's no, but I'd like confirmation.

As you have described it here:

The "normal" set up for a seat belt is the belt is tied to the frame at four points. In the driver's side, you have a point on the outside at the floor, a point inside at the floor, a point above the shoulder on the outside and again at the floor.

If this changes so there's only three points of contact, one above the shoulder, one at the outside floor and on on the inside floor, is the stress on the shoulder point any different than before in the event of an accident? The contact area over the body would be the same.

...There is no difference in the load applied to the belt running from buckle to the point over the shoulder, or that borne by the upper anchor point. The only thing that's changed is the retractor and the lead running between the retractor and the upper anchor point are both gone.

By Johnny T, Posted May 26, 2011

What.... the....

By Smacaroni, Posted May 27, 2011

Johnny, I'll post some photos when I'm done.

As you have described it here:

...There is no difference in the load applied to the belt running from buckle to the point over the shoulder, or that borne by the upper anchor point. The only thing that's changed is the retractor and the lead running between the retractor and the upper anchor point are both gone.

This is what I thought. I wanted to make sure the anchor point would still be under the same level of stress in the event of a collision. We all know that the three point belt system is better than the lap belt only, my lap belts are in not so great shape, mostly the buckle is where the problem is, so they need to be replaced.

And as I said above, getting the genuine hardware is not an easy fete.

The retractor would still be on the left side on the floor, but it would be retracting "out" instead of down, which is how the retractable lap belt operates now.